The length of a pipe with 1 T = 12.155’ ft e/c . What is e/e length if the fitting allowance is 1 3/4”inch

Find the equation of the line with slope =8 and passing through (6,53) write your equation in the form y=mx+b

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

Identify one charcteristic of exponential growth